Parametric equation of the ellipse:
Thus for any point P(x, y) on ellipse we have x = a cosθ, y = b sinθ are called as parametric equation of ellipse.
Position of a Point Relative to Ellipse:
The point P(x1, y1) is outside or inside or on ellipse 
according as the quantity 
may be positive or negative or zero.
Illustration: Consider ellipse x2 + 3y2 = 6 and a point P on it in the 1st quadrant at a distance of 2 units from centre. Find eccentric angle of P.
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Solution: The equation of ellipse is x2 + 3y2 = 6
The equation of auxiliary circle is x2 + y2 = 6
As P ≡ (x1, y1) & Q ≡ (x1, y2) lie on ellipse and circle respectively we have,
x12 + 3y12 = 6 .....(1)
x12 + y22 = 6 .....(2)
∴3y12 -y22 = 0 => 
Again OP = 2 => x12 + y12 = 4 .....(3)
By (1) -(3), we get,
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2y12 = 2 => y12 = 1 => y1 = 1 [∴ P is in the 1st quadrant]
∴y2 = √3
Putting y1 in (1), we get x12 = 3 => x1 =√3
∴ The eccentric angle of 
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